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Simplifying b2 + -5b + -4 = 0 Reorder the terms: -4 + -5b + b2 = 0 Solving -4 + -5b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5b + 4 + b2 = 0 + 4 Reorder the terms: -4 + 4 + -5b + b2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5b + b2 = 0 + 4 -5b + b2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5b + b2 = 4 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = 4 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5b + b2 = 10.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (b + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
b + -2.5 = 3.201562119 Simplifying b + -2.5 = 3.201562119 Reorder the terms: -2.5 + b = 3.201562119 Solving -2.5 + b = 3.201562119 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 3.201562119 + 2.5 b = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 b = 5.701562119 Simplifying b = 5.701562119Subproblem 2
b + -2.5 = -3.201562119 Simplifying b + -2.5 = -3.201562119 Reorder the terms: -2.5 + b = -3.201562119 Solving -2.5 + b = -3.201562119 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -3.201562119 + 2.5 b = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 b = -0.701562119 Simplifying b = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.701562119, -0.701562119}
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